Synthesis of Zero Effluent Multipurpose Batch Processes Using Effective Scheduling

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1 18 th Europan Symposium on Computr Aidd Procss Enginring ESCAPE 18 Brtrand Braunschwig and Xavir Joulia (Editors) 8 Elsvir B.V./Ltd. All rights rsrvd. Synthsis of Zro Efflunt Multipurpos Batch Procsss Using Effctiv Schduling Jacqus F. Gouws a,b, Thokozani Maozi a,c a Dpartmnt of Chmical Enginring, Univrsity of Prtoria, Lynnwood Rd, Prtoria, 0002, South Africa b Logistics and Quantitativ Mthods, CSIR Built Environmnt, P. O. Box 395, Prtoria, 0001, South Africa c Dpartmnt of Computr Scinc, Univrsity of Pannonia, Egytm u. 10, Vszprém, H-8, Hungary Abstract Wastwatr minimization in batch sss has gaind much attntion in th vry rcnt past. Mainly 2 rasons li bhind this hightnd intrst. Firstly, batch oprations ar inhrntly flxibl, which rndrs thm idal for volatil conditions that charactriz today s markts. Scondly, batch sss tnd to produc highly toxic fflunt strams, albit in rlativly small quantitis in comparison to thir continuous countrparts. Th stringnt nvironmntal conditions militat against th lattr charactristic of batch plants, hnc th nd to liminat or minimiz fflunt. In most publishd litratur, wastwatr minimization is achivd through watr rus, watr rcycl, watr rgnration rus and watr rgnration rcycl. Ths concpts gnrally xclud th possibility of watr bing usd as a ky ingrdint in th watr using oprations. Howvr, som pharmacutical and agrochmical oprations, which traditionally oprat in a batch mod, offr a uniqu opportunity to us rcycl or rus watr as th main constitunt of th final product. In som of ths oprations watr constituts mor than 90% of th final product makup. Th problm addrssd in this papr bars this fatur, which consquntly allows th batch sss to oprat in a nar-zro fflunt mod. Morovr, th qustion of th numbr and siz of th vssls usd in a batch ssing facility has always posd a problm. Th incorrct approach to th synthsis of a batch plant can lad to th situation whr ssing vssls ar ovr sizd and vn th possibility of idl ssing vssls. This could pos a possibl ovr capitalisation of an opration. In ssnc, an optimal dsign of a batch ssing plant is dtrmind by considring th schduling of oprations in th synthsis phas. Th mathmatically basd mthod prsntd in this papr dals with th synthsis of a batch plant oprating in th fashion mntiond abov. Th mthod dtrmins th optimal siz and numbr of ssing vssls and wastwatr storag vssls, whil schduling th opration in such a mannr as to oprat in a nar-zro fflunt fashion Kywords: fflunt, minimization, ss, batch. 1. Introduction Concrn ovr th impact of industry on th nvironmnt is gratr now than vr. Environmntal lgislation is bcoming vr mor stringnt in an ffort to rduc th

2 2 J. F. Gouws t al. ngativ impact industry has on th nvironmnt. Coupld with this is th fact that socity is bcoming vr mor conscious of th stat of th nvironmnt. Traditional nd-of-pip tratmnt mthods ar not always conomically viabl to mt stringnt fflunt targts. Thrfor, ss intgration tchniqus ar bcoming vr mor important in rducing th amount of fflunt producd. Wastwatr minimisation in batch sss has slowly gaind som attntion in th past fw yars. Past wastwatr mthodologis can roughly b dividd into two main catgoris, namly, graphical tchniqus [1,2,3] and mathmatical tchniqus [4,5,6,7]. Graphical tchniqus hav thir roots in graphical tchniqus dvlopd for continuous sss, whil mathmatical tchniqus hav thir roots in mathmatical programming. Past mthodologis for wastwatr minimisation in batch sss hav bn mainly focusd on mass transfr basd oprations. In such oprations watr is consumd at th bginning of a unit opration and producd at th nd. Rus btwn diffrnt units is govrnd by availability of wastwatr and th concntration of th contaminants prsnt in th wastwatr. Also, oprations do xist whr wastwatr is producd as a rsult of a claning opration. If products producd from such oprations rquir watr as a raw matrial, it should b possibl to rus th wastwatr as part of product formulation, sinc th wastwatr is only contaminatd with th rsidu in th prvious batch of th sam or anothr compatibl product. Th wastwatr, whn rusd in this mannr, is significantly rducd, hnc th plant can oprat in a nar zro fflunt fashion. Furthrmor, th rsidu prsnt in th wastwatr is rcovrd, which could provid substantial conomic bnfits. A mathmatical formulation for th synthsis of plants oprating in a nar zro fflunt mod of opration has bn dvlopd. Th formulation dtrmins th numbr and siz of ssing vssls and storag vssls, whil nsuring wastwatr is rusd as part of product. Sinc product intgrity is of paramount importanc, wastwatr containing diffrnt contaminants is not allowd to mix. Hnc, thr is a ddicatd storag vssl for ach typ of wastwatr. Furthrmor, th mthodology is drivd to tak into account oprations whr th contaminant mass in th wastwatr is ngligibl and whr it is not ngligibl. 2. Problm Statmnt Th problm addrssd in this papr can b formally statd as follows. Givn, i) rquird production ovr a givn tim horizon, ii) product rcip and production tims, iii) maximum numbr of ssing vssls and storag vssls, and iv) maximum and minimum capacity of ssing vssls and storag vssls, dtrmin th plant dsign that will minimis cost, i.. th dsign with th optimal numbr and siz of ssing vssls and storag vssls as wll as minimum fflunt gnration. 3. Mathmatical Formulation Th following sts, variabls and paramtrs ar usd in th mathmatical formulation

3 Synthsis of Zro Efflunt Multipurpos Batch Procsss Using Effctiv Schduling 3 Sts S in, = {s in, s in, = input stat into ssing vssl } J = { = ssing vssl} U = {u u = storag vssl} P = {p p = tim point} Variabls f w (s in,,p) f (s in,,p) v () v stor (u) () y(s in,,p) Paramtrs Ψ wash V min V max α β α stor β stor C mass of watr usd for a washout for stat s in, at tim point p fflunt watr from ssing vssl at tim point p capacity of ssing vssl capacity of storag vssl u xistnc binary variabl for ssing vssl binary variabl showing usag of stat s in, at tim point p factor rlating th siz of a ssing vssl to th amount of washout watr minimum capacity of a ssing vssl maximum capacity of a ssing vssl cost of a ssing vssl cost of a ssing vssl basd on siz cost of a storag vssl cost of a storag vssl basd on siz tratmnt cost of th fflunt watr 3.1. Mass balanc constraints Th first part of th mathmatical formulation constituts th mass balanc constraints. Mass balancs ar don ovr a ssing unit and a storag vssl. Th mass balancs ovr a ssing vssl can b dividd into two main groups. Th first group compriss of all th constraints rlatd to product gnration and th scond group, all th constraints rlatd to a washout. Th mass balancs rlatd to product includ a raw matrial balanc and a mass balanc ovr a ssing unit. Th raw matrial balanc nsurs that th corrct ratio of watr and othr raw matrials is usd for a product. Apart from th two balancs thr ar also capacity constraints. Th washout mass balancs compris of an inlt watr balanc and an outlt watr balanc. Th amount of watr usd for a washout is dpndnt on th siz of th ssing vssl, and is dtrmind using Equation (1), which is th inlt watr balanc. Equation (1) contains a non-linar trm that is linarisd using a Glovr transformation[8]. ( sin,, p) Ψwashv ( ) y( sin,, p), J, sin, Sin f w, = (1) Mass balancs ovr a storag vssl includ a watr balanc and if ncssary a contaminant balanc. Th formulation is capabl of daling with both th scnario whr th contaminant mass in th washout watr is ngligibl and not.

4 4 J. F. Gouws t al Schduling constraints Sinc th sss dalt with ar batch sss th inhrnt discontinuous natur has to b takn into account. Schduling constraints ar formulatd to nsur that th ssing of raw matrial occurs aftr a washout has takn plac, i.. onc a vssl has bn cland, and aftr a prvious batch has finishd ssing. Furthr constraints nsur a washout bgins dirctly aftr th product has bn rmovd from a ssing vssl. Duration constraints ar formulatd for th production and washouts. Apart from th abov constraints, th rus of watr in product also has to b schduld. Constraints ar formulatd to nsur that watr dirctly rusd btwn two ssing vssls occurs at th nd of a wash from th sourc and th bginning of th ssing of th sink. This is similar for indirct rus, howvr, in this instanc th timing of watr moving to and from a storag vssl must coincid with th nding tim of a washout and th bginning of product ssing, rspctivly. Th formulation also catrs for a maximum storag tim of washout watr in a storag vssl. Constraints ar formulatd to nsur th diffrnc btwn th inlt tim and outlt tim of watr from a storag vssl is lss than th maximum allowabl storag tim Dsign constraints Th final constraints considrd ar th dsign constraints. Th first of ths ar th xistnc constraints. An xistnc binary variabl is dfind for ach ssing vssl and ach storag vssl. If a ssing vssl sss matrial within th tim horizon thn th binary variabl is st to on. This is similar for a storag vssl. Th uppr and lowr bounds of a ssing vssls siz ar dfind using Equation (2) and similar constraint holds for a storag vssl. min max ( ) V v ( ) ( ) V J 3.4. Obctiv function Th obctiv function in th formulation is th minimisation of ovrall cost. In this instanc th ovrall cost ariss from th cost of th ssing vssls, th cost of th storag vssls and th tratmnt costs of th fflunt watr. Th obctiv function is givn in Equation (3). Th obctiv function is linar, as it was assumd that th cost of a ssing vssl and storag vssl is a linar function of th siz of th vssl. min + α sin, p C f ( ) + β v ( ) + α storstor ( u) + β stor v stor ( u) ( s, p) J, u U, s S, p P in. u in, in, (2) (3) 4. Industrial Cas Study Th mthodology was applid to an industrial cas study stmming from a pharmacuticals mixing facility. Th industrial cas study involvs th dsign of a small mixing opration that producs thr diffrnt products. Each product has a fixd ratio

5 Synthsis of Zro Efflunt Multipurpos Batch Procsss Using Effctiv Schduling 5 btwn th amount of watr usd in th product and othr raw matrials. For product 1 th ratio of watr to othr raw matrial is 80:20, for product 2 th ratio of watr to othr raw matrial is 82.5:17.5 and for product 3 th ratio is 90: kg, 6000kg and 5000kg ar rquird for products 1, 2 and 3 ovr a 24 hour tim horizon rspctivly. Th numbr and siz of batchs rquird to fulfill th production rquirmnts is not known. A maximum of 4 mixing vssls can b usd with a minimum capacity of 1000kg and a maximum capacity of 4000kg. Maximum rus opportunitis ar nsurd through th inclusion of th possibility of wastwatr storag. Thr distinct typs of wastwatr will b producd from th claning opration, du to th thr diffrnt products mixd. Each typ of wastwatr has th possibility of bing stord in a distinct storag vssl. Th minimum and maximum capacity of ach storag vssl is 500kg and 1500kg, rspctivly. Th amount of watr usd for a washout was dpndnt on th siz of th ssing vssl. For vry 1000kg incras in th mixrs siz th amount of watr usd for a washout would incras by kg. Thrfor, Ψ wash has th valu of 0.2. Th constants usd for th obctiv function ar givn in Tabl 1. Tabl 1. Cost data usd in industrial cas study Constant α Valu β 0.8 α stor 400 (c.u./mixr) 100 (c.u./storag vssl) β stor 0.5 C 5 (c.u./kg wastwatr) Th problm was formulatd in GAMS and subsquntly solvd using CPLEX. Th final dsign rquird 4 mixing vssls and no storag vssls for th wastwatr. Mixing vssls 2, 3 and 4 ach had a capacity of 1000kg and mixr 1 had a capacity of 3000kg. Th total amount of fflunt gnratd from th ss was 600kg and th obctiv function had an optimal valu of 9400 c.u. Efflunt is gnratd, sinc thr is no opportunity for furthr rus of th wastwatr at th nd of th tim horizon. Th solution tim was 7665 CPU sconds using a Pntium 4, 3.2 GHz ssor. Th problm had 423 binary variabls and 2855 continuous variabls. Th Gannt chart showing th production schdul is givn in Figur 1. Th black stripd boxs rprsnt a production and th gry boxs rprsnt a mixr bing washd. Th P in th stripd boxs rprsnts product and th numbr aftr th P rprsnts th rspctiv product numbr. Th bold numbrs rprsnt th amount of watr rusd in product. From Figur 1 on can s that mixr 2 is ddicatd to th production of product 2. This is similar for mixr 3, which is ddicatd to th production of product 3. Mixrs 1 and 4, howvr, produc batchs of all thr products. Th siz of th batchs producd from ach mixr is dtrmind by th optimal siz of th mixr, hnc th siz of th batchs from mixrs 2, 3 and 4 ar 1000kg and from mixr 1 is 3000kg. Intrsting to not is that mixr 3 dos not produc any fflunts throughout th tim horizon.

6 6 J. F. Gouws t al. Efflunt: 4 P3 P3 P1 Mixr 3 P3 P3 P3 Efflunt: Efflunt: 2 P2 P2 P P2 P Tim (hr) Figur 1. Gannt chart rprsnting th production schdul 5. Conclusions A mthodology for th synthsis of batch plants incorporating th zro fflunt mod of opration has bn prsntd. In th zro fflunt mod of opration, th wastwatr gnratd in th opration is rusd as a constitunt in a batch of subsqunt compatibl product. Th mthodology dtrmins th optimal siz and numbr of ssing vssls and wastwatr storag vssls. Th mthodology has bn applid to an industrial cas study. Th industrial cas study involvd th dsign of a pharmacuticals mixing opration that producs thr products. Th rsulting dsign for th industrial cas study had 4 mixing vssls and no wastwatr storag vssls. Thr of th mixing vssls had a capacity of 1000kg and th rmaining mixing vssl had a capacity of 3000kg. Rfrncs [1] Y. P. Wang and R. Smith, TransIChmE, 73(1995), 905. [2] D. C. Y. Foo, Z. A. Manan and Y. L. Tan, J. Clan. Prod., 13 (5), 1381 [3] T. Maozi, C. J. Brouckart and C. A. Buckly, J. Environ. Manag., 78 (6), [4] R. Grau, M. Gralls, J. Corominas, A. Espuña, and L. Puiganr, L., Comp. Chm. Eng., 20 (1996), 853 [5] M. Almató, E. Sanmartí, A. Espuńa, and L. Puiganr, Comp. Chm. Eng., 21 (1997), s971 [6] J. K. Kim and R. Smith, Procss Saf. Environ., 82 (4), 238 [7] T. Maozi, Comp. Chm. Eng., 29 (5), 1631 [8] F. Glovr, Manag. Sci., 22 (1975), 455.

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